Coercive estimates and existence of solutions for a model of one- dimensional viscoelasticity with a non-integrable memory function
In this work, the author re-examines a model one-dimensional equation of motion for viscoelastic materials with a non-integrable memory function, with the objective of developing an existence theory which exploits the parabolic character of the equation. Existence of solutions to the initial-value problem based on coercive estimates for the linearized problem, are established both for small and large smooth date. In the former case, existence of solution is proved globally in time while in the latter case it is proved locally in time. This is a clearly written paper whose results should be of interest to those working in the field of integral equations and, to a lesser extent, to those working on viscoelastic materials.
homogeneous Dirichlet boundary conditions
scientific article; zbMATH DE number 4085147